The World Cup semi-finalists claimed a dramatic 23-21 victory over Ireland in Dublin but it came at a cost.
Davies is likely to be cited for a dangerous tip-tackle on Ireland replacement Donnacha Ryan that saw him collect a yellow card from referee Wayne Barnes when it should undoubtedly have been red, Barnes having followed the recommendation of his assistant Dave Pearson.
Warburton, meanwhile, went off at half-time with a dead leg.
Italian Achille Reali, the independent match citing commissioner, has until 5pm tomorrow to make a decision on Davies, who would then face a disciplinary hearing later this week.
Wales coach Warren Gatland has admitted he is fearing the worst, with Davies likely to join injured second-row forwards Luke Charteris and Alun-Wyn Jones on the sidelines. A ban of four weeks or more cannot be ruled out. “We’ve got to plan potentially for him being cited,” Gatland said. “We have got to prepare for the worst.”
In the other match in the weekend’s opening round, France defeated Italy 30-12 at the Stade de France, with highly-rated centre Wesley Fofana amongst the try scorers.
Table-toppers France face Ireland on Saturday in Paris.